The research, led by Zhicheng Zhong and Qiang Zhao of the University of Jinan along with colleagues in China and the United Kingdom, focuses on Shandong Province, a densely populated agricultural heartland on China’s eastern coast. Spanning the years 1959 to 2023, the study constructed two comprehensive drought indices using a statistical technique known as the C-vine copula. The first, CDIPRE, is anchored in precipitation, treating rainfall as the input to the regional water cycle. The second, CDIRUN, is anchored in runoff, treating streamflow as the output of that same cycle. By building both variants, the team could directly test a deceptively simple question: does it matter whether you measure drought from the top of the water cycle or the bottom?

To understand why this question matters, it helps to grasp what a copula actually does. In hydrology, the variables that govern drought—precipitation, runoff, potential evapotranspiration, soil moisture—do not vary independently. A dry month typically follows from large-scale atmospheric patterns that also suppress soil moisture and reduce river flow. Traditional indices often sidestep these dependencies by simply averaging or weighting standardized variables, an approach that can distort the true joint behavior of the water cycle. Copulas, by contrast, are mathematical functions that describe the dependence structure between random variables separately from their individual distributions. This separation allows scientists to model how variables co-vary, including in the extremes, where drought lives. Vine copulas extend this idea to many variables by decomposing a complex multivariate dependence into a cascade of simpler pairwise building blocks, and the C-vine variant organizes those pairs around a central hub variable—in this case, either precipitation or runoff.

The choice of hub turns out to be consequential. The researchers found that both CDIPRE and CDIRUN successfully integrate information about meteorological, hydrological, and agricultural drought, overcoming the central weakness of conventional univariate indices that track only one drought type at a time. But when the two indices were compared head to head, CDIRUN—the runoff-centered index—outperformed its precipitation-based sibling in capturing the characteristics of different drought types and in assessing agricultural drought impacts. This makes physical sense. Runoff integrates everything that happens upstream in the water cycle: rainfall deficits, evaporative losses, soil moisture depletion, and the slow release of water from storage. A deficit in runoff is, in a sense, the net verdict of the entire system, whereas a precipitation deficit is only the opening statement of a drought that may or may not develop into a genuine water crisis.

The study went beyond index construction to map the geography of drought across Shandong. Using run theory, a standard framework that defines drought events as periods during which an index remains below a threshold, the team analyzed drought duration, severity, and frequency across the province. The results revealed a striking spatial pattern: CDIRUN identified longer total drought durations in the north-central parts of Shandong, while other drought characteristics showed spatial distributions that depended on the scale of analysis. This scale dependence is a reminder that drought is not a single phenomenon but a family of processes operating at different temporal and spatial resolutions, and that any monitoring system must be explicit about which scale it is interrogating.

To probe why drought varies so much from place to place, the researchers turned to Geodetector, a statistical method designed to quantify how much of the spatial heterogeneity in a variable can be explained by candidate explanatory factors. The analysis identified the input variables underlying CDIRUN—precipitation, runoff, potential evapotranspiration, and soil moisture—as the dominant drivers of spatial heterogeneity in drought across the province. In other words, the same ingredients that feed the index are the ones that govern where drought bites hardest, which lends the index a degree of internal coherence that purely empirical composites often lack.

Perhaps the most intriguing part of the study reaches beyond Shandong entirely, into the Pacific Ocean. Drought in any given region is not purely a local affair; it is steered by large-scale climate oscillations that redistribute heat and moisture across the planet. The team examined the statistical relationships between their indices and a suite of climate teleconnection indices, and found that during the study period, the North Pacific Index showed the strongest statistical correlation with CDIRUN. Digging deeper, they identified the Northern Oscillation Index combined with the North Pacific Index as the statistically optimal bivariate combination, and a three-way combination adding the Southern Oscillation Index as the optimal multivariate set. The Southern Oscillation Index, of course, is the classic yardstick of the El Niño–Southern Oscillation, the planet’s most influential year-to-year climate fluctuation. The finding suggests that drought in this part of eastern China carries the fingerprint of Pacific-wide circulation patterns, opening a door toward longer-lead drought forecasting.

The practical implications are considerable. Shandong is a major grain producer, and its agricultural economy has long been exposed to the vagaries of a variable monsoon-influenced climate. Groundwater overexploitation in the wider North China Plain has compounded the region’s vulnerability, making accurate drought assessment a matter of food security as much as academic interest. An index like CDIRUN, which responds to the integrated state of the water cycle rather than to rainfall alone, could give water managers earlier and more reliable warnings of when a meteorological dry spell is turning into a genuine hydrological and agricultural crisis. The authors position the index as a tool for drought monitoring, water resource management, and agricultural planning under climate change, and the study’s structure supports that framing.

The work also sits within a broader scientific reckoning. Recent global analyses have shown that warming is accelerating drought severity worldwide, and reviews of widely used drought indices have catalogued the challenges of assessing drought under a changing climate, where the historical statistical relationships that indices rely on may themselves be shifting. Multivariate approaches built on copula theory have gained traction precisely because they can fuse multiple strands of hydrological information without discarding their dependence structure, and studies across basins from the Yangtze to the Qinghai-Tibet Plateau have explored similar composite frameworks. What distinguishes the new study is its systematic comparison of two anchoring strategies within the same copula framework, applied over a sixty-five-year record in a region where the stakes are high.

There are, as always, caveats and open questions. The analysis is regional, and the relative merits of runoff-centered versus precipitation-centered anchoring may differ in basins with different geology, land use, or degrees of human regulation. Runoff in heavily managed systems is shaped by reservoirs, irrigation withdrawals, and diversions, which can decouple it from the natural water cycle in ways that complicate interpretation. The authors note that data will be made available on request, and the study was supported by the National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province. Still, the central message is likely to travel well beyond one province: drought assessment improves when it follows water through the entire cycle, from the sky to the soil to the stream. As climate change tightens the screws on regional water budgets, the indices we trust may need to look less like rain gauges and more like the water cycle itself.

Subject of Research: Copula-based multivariate drought indices integrating precipitation and runoff within the hydrological cycle

Article Title: Hydrological cycle-based comprehensive drought assessment: a comparative study of precipitation-centered cdipre and runoff-centered CDIRUN indices via c-vine copula

Article References: Zhong, Z., Zhao, Q., Xue, J., Dou, X., Zhao, Y., Wang, J., Liu, J., & Zhao, M. (2026). Hydrological cycle-based comprehensive drought assessment: a comparative study of precipitation-centered cdipre and runoff-centered CDIRUN indices via c-vine copula. Theoretical and Applied Climatology, 157(10), Article 608. https://doi.org/10.1007/s00704-026-06535-x

Image Credits: AI Generated

DOI: 10.1007/s00704-026-06535-x

Keywords: drought, hydrological cycle, vine copula, runoff, precipitation, Shandong Province, climate teleconnections, North Pacific Index, soil moisture, agricultural drought, water resource management, climate change